Sir Alex says Arsenal will pose an even greater threat to United this season, despite losing Thierry Henry.
Henry, long considered one of the finest talents in the Premier League and a two-time FIFA World Player of the Year runner-up, left the Gunners last month to join Spanish giants Barcelona.
But while many believe the London club will struggle without the 29-year-old, the United boss says Arsenal will emerge stronger.
"I think it was time for him to go," Sir Alex told reporters at a Labour Party football dinner at Wembley Stadium on Thursday night.
"I think Arsene [Wenger] knew that and I think they'll be better. Without question, I'm more convinced that they'll be in the top four without Henry."
The Frenchman scored nine times in 15 appearances against the Reds during his Arsenal career, including a last-minute winner in January 2007 at the Emirates Stadium.
The United boss also laughed off claims from Chelsea manager Jose Mourinho that he would be under intense pressure to achieve results having spent heavily in the transfer market this summer.
"It's an amazing statement actually," he said. "I don't think he knows I've been here for 20 years. Whether he is trying to transfer some of the pressure - maybe he's under pressure himself, I don't know. I thought it was quite funny."